1. Field of the Invention
The invention relates to methods for determining dissociation constants.
2. Description of the Related Technology
Proteins are vital parts of living organisms, as they are the main components of the physiological metabolic pathways of cells. Quantification of protein-protein and protein-mRNA interactions is an important step towards understanding the physiological metabolic pathways. A key parameter that characterizes the strength of any protein-protein or protein-mRNA interaction is the equilibrium dissociation constant, Kd (in units of molar (M)) between the two molecules. Traditionally, Kd is measured using equilibrium dialysis through a semipermeable membrane, which is tedious and time consuming.
Alternatively, one can use a surface plasma resonance (SPR) instrument, such as the optical sensor offered by Biacore, to measure Kd. However, such optical sensors are expensive and many laboratories do not have access to an optical sensor capable of SPR.
In this disclosure, we show that the dissociation constant, Kd, between two molecules can be easily and accurately measured using piezoelectric microcantilever sensors (PEMS). The advantage of the PEMS methodology is low-cost. In addition, the PEMS measurement is rapid and label-free.
U.S. Pat. No. 2006/0065046 (Battiston) suggests a method for measuring binding constants, association or dissociation constants by measuring a piezoelectric microcantilever deflection in a stagnant body of analyte liquid and measuring deflection as a function of time for a flowing body of analyte liquid. Battiston, however, fails to provide details regarding how the dissociation constant is calculated.
U.S. Pat. No. 6,033,913 (Morozov) discloses a method for determining ligand interaction with macromolecules, such as proteins. In Example 1, a cantilever sensor was allowed to contact a ligand and glucose solution. Morozov estimated the binding constant from a graph of tension as a function of time for various glucose solution concentrations. By graphing the inverse tension changes of the cantilever sensor as a function of the inverse glucose concentration, Morozov was able to calculate the dissociation constant. Morozov's method, however, does not use a piezoelectric microcantilever.
Piezoelectric microcantilever sensors (PEMS) consisting of a highly piezoelectric layer bonded to a nonpiezoelectric layer are a new type of biosensors whose mechanical resonance can both be excited and detected by electrical means. With receptors immobilized on the PEMS surface, binding of antigens shifts PEMS resonance frequency. Real-time, label-free antigen detection is achieved by electrically monitoring the PEMS resonance frequency shift. J. W. Yi, W. Y. Shih, and W. H. Shih, “Effect of length, width, and mode on the mass detection sensitivity of piezoelectric unimorph cantilevers,” J Appl. Phys. 91 (3), 1680 (2002). PEMS detection sensitivity is strongly related to the thickness and the size of the PEMS. Generally, a PEMS detection sensitivity increases with a reduced PEMS size and thickness. For example, a lead zirconate titanate (PZT)/glass PEMS about 1 mm long consisting of a 127 μm commercial PZT layer on a 75-150 μm glass layer with a 2 mm long glass tip generally exhibited a mass detection sensitivity on the order of 10−10 g/Hz. Q. Zhu, W. Y. Shih, and W.-H. Shih, “Real-Time, Label-Free, All-Electrical Detection of Salmonella typhimurium Using Lead Titanate Zirconate/Gold-Coated Glass Cantilevers at any Relative Humidity,” Sensors and Actuators B, 125, 379-388 (2007), Q. Zhu, W. Y. Shih, and W.-H. Shih, “In-Situ, In-Water Detection of Salmonella typhimurium Using Lead Titanate Zirconate/Gold-Coated Glass Cantilevers at any Dipping Depth,” Biosensors and Bioelectronics, 22, 3132 (2007), J.-P. McGovern, W. Y. Shih, R. Rest, M. Purohit, Y. Pandia, and W.-H. Shih, “Label-Free Flow-Enhanced Specific Detection of Bacillus anthracis Detection Using a Piezoelectric Microcantilever Sensor,” The Analyst, 132, 649-654 (2008), J. Capobianco, W. Y. Shih, and W. H. Shih, “3-Mercaptopropyltrimethoxysilane as Insulating Coating and Surface for Protein Immobilization for Piezoelectric Microcantilever Sensors,” Rev. Sci. Instr., 78, 046106 (2007), and J. Capobianco, W. Y. Shih, W.-H. Shih, Q.-A. Yuan, and G. P. Adams, “Label-free, All-electrical, In-Situ Human Epidermal Growth Receptor-2 Detection,” Rev. Sci. Instrum. 79, 076101 (2008). A lead magnesium niobate-lead titanate, (PbMg1/3Nb2/3O3)0.63—(PbTiO3)0.37 (PMN-PT)/tin PEMS 600-1200 μm long consisting of an 8 μm thick PMN-PT layer bonded with a 5 μm thick tin layer exhibited a mass detection sensitivity on the order of 10−12-10−13 g/Hz. J.-P. McGovern, W. Y. Shih, and W.-H. Shih, “In-Situ Detection of Bacillus Anthracis Spores Using Fully Submersible, Self-Exciting, Self-Sensing PMN-PT/Sn Piezoelectric Microcantilevers,” The Analyst, 132, 777-783 (2007) and a PZT/SiO2 60 μm long consisting of a 1 μm thick PZT thin film on 1 μm thick SiO2 layer with a 20 μm long SiO2 tip exhibited a mass sensitivity of 10−16 g/Hz. Z. Shen, W. Y. Shih, and W.-H. Shih, “Self-Exciting, Self-Sensing PZT/SiO2 Piezoelectric Microcantilever Sensors with Femtogram/Hz Sensitivity,” Appl. Phys. Lett., 89, 023506 (2006). Due to thickness and size differences, for Her2 detection, with the same single-chain variable fragment (scFv) antibody, H3, immobilized on the PEMS 3-mercaptopropyltrimethoxysilane (MPS) insulation surface, a 127-μm thick PZT/glass PEMS exhibited only a μg/ml concentration sensitivity while an 8-μm thick PMN-PT PEMS exhibited a much lower, clinically relevant 5 ng/ml concentration sensitivity, both in a background of 1 mg/ml of bovine serum albumin (BSA) using lower-frequency flexural modes.
As shown by more recent studies, Q. Zhu, W. Y. Shih, and W.-H. Shih, “Mechanism of Flexural Resonance Frequency Shift of a Piezoelectric Microcantilever Sensor during Humidity Detection,” Appl. Phys. Lett. 92, 183505 (2008) and Q. Zhu, W. Y. Shih, and W.-H. Shih, “Length and Thickness Dependence of Longitudinal Flexural Resonance Frequency Shifts of a Piezoelectric Microcantilever Sensor due to Young's Modulus Change,” J. Appl. Phys. 104, 074503 (2008). PEMS detection resonance frequency shift was primarily due to the elastic modulus change in the piezoelectric layer from the binding-induced surface stress. As a result, the mass sensitivity of a PMN-PT PEMS and that of a PZT PEMS were respectively 300 times and 100 times higher than could be accounted for by mass loading alone. With a DC bias electric field, the mass sensitivity of a PMN-PT PEMS could even be further enhanced to more than 1000 times higher than could be accounted for by mass loading alone. Q. Zhu, W. Y. Shih, and W.-H. Shih, “Enhanced Detection Resonance Frequency Shift of a Piezoelectric Microcantilever Sensor by a DC Bias Electric Field in Humidity Detection,” Sensors and Actuators, B 138, 1 (2009). These studies also revealed that due to the presence of the highly piezoelectric layer, PEMS could exhibit high-frequency non-flexural resonance modes such as width, length and thickness extension modes that silicon-based microcantilevers lack. Q. Zhu, W. Y. Shih, and W.-H. Shih, “Mechanism of the Flexural Resonance Frequency Shift of a Piezoelectric Microcantilever Sensor in a DC Bias Electric Field,” Appl. Phys. Lett. 92, 033503 (2008).
At the same time, it was also shown that as a result of the elastic modulus change mechanism, a PEMS relative resonance frequency shift, Δf/f, was directly proportional to the binding-induced surface stress and inversely proportional to the PEMS thickness where Δf and f denotes a PEMS resonance frequency shift and resonance frequency, respectively. This suggests that under the same detection conditions, Δf could be higher with a high-frequency resonance mode to result in higher detection sensitivity. As non-flexural extension mode resonance occur at a much higher frequency than flexural-mode resonance, detection using non-flexural resonance modes potentially can increase PEMS sensitivity without size reduction.